Problem: Solve for $x$ : $ 3|x + 9| + 8 = -3|x + 9| + 2 $
Answer: Add $ {3|x + 9|} $ to both sides: $ \begin{eqnarray} 3|x + 9| + 8 &=& -3|x + 9| + 2 \\ \\ { + 3|x + 9|} && { + 3|x + 9|} \\ \\ 6|x + 9| + 8 &=& 2 \end{eqnarray} $ Subtract ${8}$ from both sides: $ \begin{eqnarray} 6|x + 9| + 8 &=& 2 \\ \\ { - 8} &=& { - 8} \\ \\ 6|x + 9| &=& -6 \end{eqnarray} $ Divide both sides by ${6}$ $ \dfrac{6|x + 9|} {{6}} = \dfrac{-6} {{6}} $ Simplify: $ |x + 9| = -1$ The absolute value cannot be negative. Therefore, there is no solution.